Capturing the Regime-Switching and Memory Properties of Interest Rates

We propose a mean-reverting interest rate model whose mean-reverting level, speed of mean-reversion and volatility are all modulated by a weak Markov chain (WMC). This model features a simple way to capture the regime-switching evolution of the parameters as well as the memory property of the data. Concentrating on the second-order WMC framework, we derive the filters of the WMC and other auxiliary processes through a change of reference probability measure. Optimal estimates of model parameters are provided by employing the EM algorithm. The <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$h$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>h</mi> </math> </EquationSource> </InlineEquation>-step ahead forecasts under our proposed set-up are examined and compared with those under the usual Markovian regime-switching framework. We obtain better goodness-of-fit performance based on our numerical results generated from the implementation of WMC-based filters to a 10-year dataset of weekly short-term-maturity Canadian yield rates. Some statistical inference issues of the proposed modelling approach are also discussed. Copyright Springer Science+Business Media New York 2014